Finite Group Databasebeta

← #497×D149 #34055127

Subgroups — #497×D149 #34055127

Order 19072.

564 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 564 conjugacy classes of subgroups — too many to draw. Only its 145 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q16×D149C212yesmaximal, complemented
2C2×SD16×D149C212yesmaximal
3C4⋊Q8×D149C211yesmaximal, characteristic, complemented
4#124×D149C211yesmaximal, characteristic
5#23750020C211yesmaximal, characteristic, complemented
6#23750019C211yesmaximal, characteristic, complemented
7#23750018C212yesmaximal, complemented
8#23750017C211yesmaximal, characteristic, complemented
9#23750016C212yesmaximal, complemented
10#97×D149C211yesmaximal, characteristic, complemented
11#497×C149C211yesmaximal, characteristic, complemented
12C2×Q8×D149C2211yescharacteristic
13C2×Q8×D149C2212yes—
14C2×D4×D149C2211yescharacteristic
15C2×Dic596C2212yescomplemented
16C2×#14558726C2212yescomplemented
17C2×#14558726C2212yescomplemented
18Q16×D149—28no—
19C2×#14558725C2212yes—
20C2×#14558724C2212yes—
21C2×#14558723C2212yes—
22SD16×D149—28no—
23C2×C8×D149C2212yes—
24#18011911C2211yescharacteristic, complemented
25#18011910—22no—
26#18011909C2212yescomplemented
27#18011900C2211yescharacteristic
28#18011899C2211yescharacteristic
29#18011898C2211yescharacteristic
30#18011897—22no—
31C4⋊C4×D149—22no—
32C22⋊C4×D149—22no—
33C42×D149C2211yescharacteristic
34#18011822C2211yescharacteristic, complemented
35#18011821C2212yescomplemented
36C2×Q16×C149C2212yescomplemented
37C2×SD16×C149C2212yes—
38C4⋊Q8×C149C2211yescharacteristic, complemented
39#124×C149C2211yescharacteristic
40#97×C149C2211yescharacteristic, complemented
41C23×D149—21no—
42C2×Dic298—22no—
43C2×Dic298—21no—
44C2×Dic298C2312yes—
45C2×Dic298C2311yescharacteristic
46Q8×D149—24no—
47Q8×D149—24no—
48Q8×D149—24no—
49C2×D596C2311yescharacteristic
50C2×C22⋊D149—21no—
51D4×D149—24no—
52C2×C4×D149—21no—
53C2×C4×D149—22no—
54C2×C4×D149D412yes—
55C2×C4×D149C2311yescharacteristic
56Dic596—24no—
57#14558726—24no—
58#14558726—24no—
59#14558725—24no—
60#14558724—24no—
61#14558723—24no—
62C2×#11924746C2312yes—
63C8×D149D418yes—
64C4⋊Dic149—22no—
65#14558715—24no—
66C22⋊Dic149—22no—
67#14558713—22no—
68#14558713—22no—
69C4×Dic149D412yes—
70C4×Dic149C2311yescharacteristic
71C2×Q8×C149C2312yes—
72C2×Q8×C149C2311yescharacteristic
73C2×D4×C149C2311yescharacteristic
74Q16×C149—24no—
75SD16×C149—24no—
76C2×C8×C149C2312yes—
77C4⋊C4×C149—22no—
78C22⋊C4×C149—22no—
79C42×C149C2311yescharacteristic
80C22×D149—21no—
81C22×D149—42no—
82C22×D149—44no—
83C22×D149C2×D411yescharacteristic
84Dic298—22no—
85Dic298—22no—
86Dic298—22no—
87Dic298—44no—
88Dic298—42no—
89D596—22no—
90C22⋊D149—42no—
91C2×Dic149—21no—
92C2×Dic149—22no—
93C2×Dic149C2×D412yes—
94C2×Dic149C2×D411yescharacteristic
95C4×D149—24no—
96C4×D149—42no—
97C4×D149—44no—
98C4×D149C2×D414yes—
99#11924746C2×D414yes—
100C23×C149—21no—
101Q8×C149—22no—
102Q8×C149—22no—
103Q8×C149—22no—
104D4×C149—22no—
105C2×C4×C149—21no—
106C2×C4×C149—22no—
107C2×C4×C149C2×D412yes—
108C2×C4×C149C2411yescharacteristic
109C8×C149C2×D414yes—
110C22×C149—41no—
111C22×C149—42no—
112C22×C149C22×D411yescharacteristic
113C2×D149—41no—
114C2×D149—42no—
115C2×D149—84no—
116C2×D149#12712yes—
117C2×D149#13714yes—
118C4×C149—22no—
119C4×C149—41no—
120C4×C149—42no—
121C4×C149C22×D412yes—
122Dic149—22no—
123Dic149—41no—
124Dic149—42no—
125Dic149#12712yes—
126C2×C149—81no—
127C2×C149C2×#12711yescharacteristic
128C2×C149C2×#13712yes—
129D149—81no—
130D149#49714yesdirect product factor
131C149C2×#49711yescharacteristic, complemented, Sylow
132C2×#497—1491nomaximal, Sylow
133C22×Q16—1492no—
134C22×SD16—1492no—
135C2×C4⋊Q8—1491no—
136C2×#124—1491no—
137#497—1492no—
138#497—1492no—
139#497—1491no—
140#497—1491no—
141#497—1491no—
142#497D14911yescharacteristic, direct product factor
143C2×#97—1491no—
144C22×Q8—1491no—
145C22×Q8—1492no—
146C22×D4—1491no—
147C2×Q16—2988no—
148C2×Q16—1492no—
149C2×Q16—1492no—
150C2×Q16—1492no—
151C2×Q16C2×D14912yescomplemented
152C2×SD16—2988no—
153C2×SD16—1492no—
154C2×SD16—1492no—
155C2×SD16—1492no—
156C2×SD16C2×D14912yes—
157C22×C8—1492no—
158C4⋊Q8—2982no—
159C4⋊Q8—1492no—
160C4⋊Q8—1491no—
161C4⋊Q8C2×D14911yescharacteristic, complemented
162#124—2982no—
163#124—1491no—
164#124—1491no—
165#124—1491no—
166#124C2×D14911yescharacteristic
167C2×C4⋊C4—2982no—
168C2×C22⋊C4—2982no—
169C2×C42—1491no—
170#97—1492no—
171#97—1491no—
172#97C2×D14911yescharacteristic, complemented
173C24—2981no—
174C2×Q8—2981no—
175C2×Q8—2982no—
176C2×Q8—2984no—
177C2×Q8—2984no—
178C2×Q8—2984no—
179C2×Q8—1491no—
180C2×Q8—1492no—
181C2×Q8C22×D14911yescharacteristic
182C2×Q8C22×D14912yes—
183C2×D4—2984no—
184C2×D4—2981no—
185C2×D4—1491no—
186C2×D4C22×D14911yescharacteristic
187C22×C4—2981no—
188C22×C4—2982no—
189C22×C4—1492no—
190C22×C4—1491no—
191Q16—24no—
192Q16—2984no—
193Q16—2984no—
194Q16—2984no—
195SD16—24no—
196SD16—2984no—
197SD16—2984no—
198SD16—2984no—
199C2×C8—1492no—
200C2×C8—1498no—
201C2×C8C22×D14912yes—
202C4⋊C4—22no—
203C4⋊C4—2984no—
204C4⋊C4—2982no—
205C22⋊C4—22no—
206C22⋊C4—2982no—
207C22⋊C4—2982no—
208C22⋊C4—2982no—
209C42—1492no—
210C42—1491no—
211C42C22×D14911yescharacteristic
212C23—21no—
213C23—2981no—
214C23—5962no—
215C23—5964no—
216C23—1491no—
217Q8—22no—
218Q8—22no—
219Q8—22no—
220Q8—2982no—
221Q8—2982no—
222Q8—2982no—
223Q8—5962no—
224Q8—5964no—
225D4—22no—
226D4—2982no—
227D4—5962no—
228C2×C4—21no—
229C2×C4—22no—
230C2×C4—2984no—
231C2×C4—2981no—
232C2×C4—2982no—
233C2×C4—5962no—
234C2×C4—5964no—
235C2×C4—1492no—
236C2×C4—1491no—
237C2×C4—1494no—
238C2×C4D4×D14912yes—
239C2×C4C23×D14911yescharacteristic
240C8—1494no—
241C8D4×D14914yes—
242C22—42no—
243C22—41no—
244C22—5962no—
245C22—5961no—
246C22—1494no—
247C22—1492no—
248C22—11924no—
249C22C2×D4×D14911yescharacteristic
250C4—22no—
251C4—41no—
252C4—42no—
253C4—2982no—
254C4—5961no—
255C4—5962no—
256C4—1492no—
257C4C2×D4×D14912yes—
258C2—81no—
259C2—1494no—
260C2—11921no—
261C2#127×D14911yescharacteristic
262C2#137×D14912yes—
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#497×C149C2
socleC22×C149C22×D4
prime radicalC2×D4×D149C22
hypercenter#497D149
hypocenterC149C2×#497
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #497

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×Q16×D149C2semidirect
3. C4⋊Q8×D149C2semidirect
5. #23750020C2semidirect
6. #23750019C2semidirect
7. #23750018C2semidirect
8. #23750017C2semidirect
9. #23750016C2semidirect
10. #97×D149C2semidirect
11. #497×C149C2semidirect
15. C2×Dic596C22semidirect
16. C2×#14558726C22semidirect
17. C2×#14558726C22semidirect
24. #18011911C22semidirect
26. #18011909C22semidirect
34. #18011822C22semidirect
35. #18011821C22semidirect
36. C2×Q16×C149C22semidirect
38. C4⋊Q8×C149C22semidirect
40. #97×C149C22semidirect
130. D149#497direct (N × H)
131. C149C2×#497semidirect
142. #497D149direct (N × H)
151. C2×Q16C2×D149semidirect
161. C4⋊Q8C2×D149semidirect
172. #97C2×D149semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×Q16×D1492
C2×SD16×D1492
C4⋊Q8×D1492
#124×D1492
#237500202
#237500192
#237500182
#237500172
#237500162
#97×D1492
#497×C1492
C2×#497149